On Universal Sampling Recovery in the Uniform Norm

IF 0.4 4区数学 Q4 MATHEMATICS

Proceedings of the Steklov Institute of Mathematics Pub Date : 2024-03-06 DOI:10.1134/s0081543823050139

V. N. Temlyakov

引用次数: 0

Abstract

It is known that results on universal sampling discretization of the square norm are useful in sparse sampling recovery with error measured in the square norm. In this paper we demonstrate how known results on universal sampling discretization of the uniform norm and recent results on universal sampling representation allow us to provide good universal methods of sampling recovery for anisotropic Sobolev and Nikol’skii classes of periodic functions of several variables. The sharpest results are obtained in the case of functions of two variables, where the Fibonacci point sets are used for recovery.

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论统一规范中的普遍采样恢复

摘要众所周知，关于平方法通用采样离散化的结果对于以平方法测量误差的稀疏采样恢复非常有用。在本文中，我们证明了关于均匀法通用抽样离散化的已知结果和关于通用抽样表示的最新结果如何使我们能够为各向异性的 Sobolev 和 Nikol'skii 类几个变量的周期函数提供良好的通用抽样恢复方法。在使用斐波那契点集来恢复两个变量的函数时，我们得到了最清晰的结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Proceedings of the Steklov Institute of Mathematics MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

0.90

自引率

20.00%

发文量

审稿时长

4-8 weeks

期刊介绍： Proceedings of the Steklov Institute of Mathematics is a cover-to-cover translation of the Trudy Matematicheskogo Instituta imeni V.A. Steklova of the Russian Academy of Sciences. Each issue ordinarily contains either one book-length article or a collection of articles pertaining to the same topic.